arXiv subjects

Dirk Helbing

Publications and source records attributed to Dirk Helbing.

At least 181 records · Page 10Linked to original sources

arXiv1999

Phase Diagram of Traffic States in the Presence of Inhomogeneities

We present a phase diagram of the different kinds of congested traffic that are triggered by disturbances when passing ramps or other spatial inhomogeneities of a freeway. The simulation results obtained by the nonlocal, gas-kinetic-based traffic model are in good agreement with empirical findigs. They allow to understand the observed trasitions between free and various kinds of congested traffic, among them localized clusters, stop-and-go waves, and different types of ``synchronized'' traffic. The proposed conditions for the existence of these states suggest that the phase diagram is universal for a class of different microscopic and macroscopic traffic models.

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arXiv1999

Self-Organised Optimality in Driven Systems with Symmetrical Interactions

Extremal principles are fundamental in our interpretation of phenomena in nature. One of the best known examples is the second law of thermodynamics, governing most physical and chemical systems and stating the continuous increase of entropy in closed systems. Biological and social systems, however, are usually open and characterised by self-organised structures. Being results of an evolutionary optimisation process, one may conjecture that such systems use resources like energy very efficiently, but there is no proof for this. Recent results on driven systems indicate that systems composed of competing entities tend to reach a state of self-organised optimality associated with minimal interaction or minimal dissipation, respectively. Using concepts from non-equilibrium thermodynamics and game theoretical ideas, we will show that this is universal to an even wider class of systems which, generally speaking, have the ability to reach a state of maximal overall ``success''. This principle is expected to be relevant for driven systems in physics, but its main significance concerns biological and social systems, for which only a limited number of quantitative principles are available yet.

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arXiv1999

Cellular Automata Simulating Experimental Properties of Traffic Flows

A model for 1D traffic flow is developed, which is discrete in space and time. Like the cellular automaton model by Nagel and Schreckenberg [J. Phys. I France 2, 2221 (1992)], it is simple, fast, and can describe stop-and-go traffic. Due to its relation to the optimal velocity model by Bando et al. [Phys. Rev. E 51, 1035 (1995)], its instability mechanism is of deterministic nature. The model can be easily calibrated to empirical data and displays the experimental features of traffic data recently reported by Kerner and Rehborn [Phys. Rev. E 53, R1297 (1996)].

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arXiv1999

Explanation of Observed Features of Self-Organization in Traffic Flow

Based on simulations with the ``intelligent driver model'', a microscopic traffic model, we explain the recently discovered transition from free over ``synchronized'' traffic to stop-and-go patterns [B. S. Kerner, Phys. Rev. Lett. 81, 3797 (1998)]. We obtain a nearly quantitative agreement with empirical findings such as the ``pinch effect'', the flow-density diagram, the emergence of stop-and-go waves from nonhomogeneous congested traffic, and the dimensions of their wavelength.

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arXiv1999

Derivation, Properties, and Simulation of a Gas-Kinetic-Based, Non-Local Traffic Model

We derive macroscopic traffic equations from specific gas-kinetic equations, dropping some of the assumptions and approximations made in previous papers. The resulting partial differential equations for the vehicle density and average velocity contain a non-local interaction term which is very favorable for a fast and robust numerical integration, so that several thousand freeway kilometers can be simulated in real-time. The model parameters can be easily calibrated by means of empirical data. They are directly related to the quantities characterizing individual driver-vehicle behavior, and their optimal values have the expected order of magnitude. Therefore, they allow to investigate the influences of varying street and weather conditions or freeway control measures. Simulation results for realistic model parameters are in good agreement with the diverse non-linear dynamical phenomena observed in freeway traffic.

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arXiv1999

Generalized Force Model of Traffic Dynamics

Floating car data of car-following behavior in cities were compared to existing microsimulation models, after their parameters had been calibrated to the experimental data. With these parameter values, additional simulations have been carried out, e.g. of a moving car which approaches a stopped car. It turned out that, in order to manage such kinds of situations without producing accidents, improved traffic models are needed. Good results have been obtained with the proposed generalized force model.

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arXiv1999

Global Phase Diagram of a One-Dimensional Driven Lattice Gas

We investigate the non-equilibrium stationary state of a translationally invariant one-dimensional driven lattice gas with short-range interactions. The phase diagram is found to exhibit a line of continuous transitions from a disordered phase to a phase with spontaneous symmetry breaking. At the phase transition the correlation length is infinite and density correlations decay algebraically. Depending on the parameters which define the dynamics, the transition either belongs to the universality class of directed percolation or to a universality class of a growth model which preserves the local minimal height. Consequences of some mappings to other models, including a parity-conserving branching-annihilation process are briefly discussed.

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arXiv1999

Coherent Moving States in Highway Traffic (Originally: Moving Like a Solid Block)

Recent advances in multiagent simulations have made possible the study of realistic traffic patterns and allow to test theories based on driver behaviour. Such simulations also display various empirical features of traffic flows, and are used to design traffic controls that maximise the throughput of vehicles in heavily transited highways. In addition to its intrinsic economic value, vehicular traffic is of interest because it may throw light on some social phenomena where diverse individuals competitively try to maximise their own utilities under certain constraints. In this paper, we present simulation results that point to the existence of cooperative, coherent states arising from competitive interactions that lead to a new phenomenon in heterogeneous highway traffic. As the density of vehicles increases, their interactions cause a transition into a highly correlated state in which all vehicles practically move with the same speed, analogous to the motion of a solid block. This state is associated with a reduced lane changing rate and a safe, high and stable flow. It disappears as the vehicle density exceeds a critical value. The effect is observed in recent evaluations of Dutch traffic data.

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arXiv1999

Macroscopic Simulation of Widely Scattered Synchronized Traffic States

Recently, a phase transition to synchronized congested traffic has been observed in empirical highway data [B. S. Kerner and H. Rehborn, Phys. Rev. Lett. 79, 4030 (1997)]. This hysteretic transition has been described by a non-local, gas-kinetic-based traffic model [D. Helbing and M. Treiber, Phys. Rev. Lett. 81, 3042 (1998)] that, however, did not display the wide scattering of synchronized states. Here, it is shown that the latter can be reproduced by a mixture of different vehicle types like cars and trucks. The simulation results are in good agreement with Dutch highway data.

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arXiv1998

Jams, Waves, and Clusters

Have you been suffering from traffic jams lately and asking yourself why freeways are no free ways anymore? After several great advances in traffic theory, Korean physicists have now offered an interpretation of a recently discovered state of congested traffic, called ``synchronized'' traffic. Their fluid-dynamic simulations can be a useful tool for an optimization of traffic flow on motorways.

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arXiv1998

Optimizing Traffic Flow

We present an economics-based method for deciding the optimal rates at which vehicles are allowed to enter a highway. The method exploits the naturally occuring fluctuations of traffic flow and is flexible enough to adapt in real time to the transient flow characteristics of road traffic. Simulations based on realistic parameter values show that this strategy is feasible for naturally occuring traffic, and that even far from optimality, injection policies can improve traffic flow. Our results also allow a better understanding of the high flows observed in ``synchronized'' congested traffic close to ramps.

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arXiv1998

Traffic Data and Their Implications for Consistent Traffic Flow Modeling

The paper analyzes traffic data of the Dutch freeway A9 with respect to certain aspects which are relevant for traffic flow modeling as well as the calibration of model parameters and functions. Apart from the dynamic velocity distribution, the density-dependence and the temporal evolution of various, partly lane-specific quantities is investigated. The results are well compatible with recent macroscopic traffic flow models which have been derived from the dynamics of driver-vehicle units. These have also solved the inconsistencies, which previous models have been criticized for.

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arXiv1998

From Microscopic to Macroscopic Traffic Models

The paper presents a systematic derivation of macroscopic equations for freeway traffic flow from an Enskog-like kinetic approach. The resulting fluid-dynamic traffic equations for the spatial density, average velocity, and velocity variance of vehicles are compared to equations, which can be obtained from a microscopic force model of individual vehicle motion. Simulation results of the models are confronted with empirical traffic data.

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arXiv1998

Self-Organization Phenomena in Pedestrian Crowds

Pedestrian crowds can very realistically be simulated with a social force model which describes the different influences affecting individual pedestrian motion by a few simple force terms. The model is able to reproduce the emergence of several empirically observed collective patterns of motion. These self-organization phenomena can be utilized for new flow optimization methods which are indispensable for skilful town- and traffic-planning.

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arXiv1998

Structure and Instability of High-Density Equations for Traffic Flow

Similar to the treatment of dense gases, fluid-dynamic equations for the dynamics of congested vehicular traffic are derived from Enskog-like kinetic equations. These contain additional terms due to the anisotropic vehicle interactions. The calculations are carried out up to Navier-Stokes order. A linear instability analysis indicates an additional kind of instability compared to previous macroscopic traffic models. The relevance for describing granular flows is outlined.

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arXiv1998

Modeling and Simulation of Multi-Lane Traffic Flow

A most important aspect in the field of traffic modeling is the simulation of bottleneck situations. For their realistic description a macroscopic multi-lane model for uni-directional freeways including acceleration, deceleration, velocity fluctuations, overtaking and lane-changing maneuvers is systematically deduced from a gas-kinetic (Boltzmann-like) approach. The resulting equations contain corrections with respect to previous models. For efficient computer simulations, a reduced model delineating the coarse-grained temporal behavior is derived and applied to bottleneck situations.

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arXiv1998

Active Walker Model for the Formation of Human and Animal Trail Systems

Active walker models have recently proved their great value for describing the formation of clusters, periodic patterns, and spiral waves as well as the development of rivers, dielectric breakdown patterns, and many other structures. It is shown that they also allow to simulate the formation of trail systems by pedestrians and ants, yielding a better understanding of human and animal behavior. A comparison with empirical material shows a good agreement between model and reality. Our trail formation model includes an equation of motion, an equation for environmental changes, and an orientation relation. It contains some model functions, which are specified according to the characteristics of the considered animals or pedestrians. Not only the kind of environmental changes differs: Whereas pedestrians leave footprints on the ground, ants produce chemical markings for their orientation. Nevertheless, it is more important that pedestrians steer towards a certain destination, while ants usually find their food sources by chance, i.e. they reach their destination in a stochastic way. As a consequence, the typical structure of the evolving trail systems depends on the respective species. Some ant species produce a dendritic trail system, whereas pedestrians generate a minimal detour system. The trail formation model can be used as a tool for the optimization of pedestrian facilities: It allows urban planners to design convenient way systems which actually meet the route choice habits of pedestrians.

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arXiv1998

Fundamentals of Traffic Flow

From single vehicle data a number of new empirical results concerning the density-dependence of the velocity distribution and its moments as well as the characteristics of their temporal fluctuations have been determined. These are utilized for the specification of some fundamental relations of traffic flow and compared with existing traffic theories.

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